Instead of directly modifying an FFT algorithm for these cases, DCTs / DSTs can also be computed via FFTs of real data combined with O ( N ) pre / post processing.

Instead, a stable algorithm for solving this more general problem can for example be a divide and conquer algorithm where the array is recursively split into two parts for which the sum is calculated respectively, and where these two sums then are summed together to give the final sum.

Instead of making multiple mutated copies of a generic algorithm, an object oriented approach would abstract the algorithm into a reusable encapsulated class.

Instead, one can compute a length -( N – 1 ) cyclic convolution exactly by zero-padding it to a length of at least 2 ( N – 1 )– 1, say to a power of two, which can then be evaluated in O ( N log N ) time without the recursive application of Rader's algorithm.

Instead, the following algorithm is what actually happens:

Instead, the microcode implements part of the marking portion of Edsger Dijkstra's on-the-fly parallel garbage collection algorithm ( a mark-sweep style collector ).

Instead of that, a modified BCJR algorithm is used.

Instead, they take a user's request, pass it to several other heterogeneous databases and then compile the results in a homogeneous manner based on a specific algorithm.

Instead of trying to learn explicit features that characterize keyphrases, the TextRank algorithm exploits the structure of the text itself to determine keyphrases that appear " central " to the text in the same way that PageRank selects important Web pages.

Instead of an exchange evaluator, this version used a capture search algorithm.

Instead, a procedural generation algorithm is used which generates each landscape from a small data packet, presumably the landscape's 4-digit number ( since there are 10 unique digits and 10 ^ 4

Instead of looking at the total sequence, the Smith – Waterman algorithm compares segments of all possible lengths and optimizes the similarity measure.

Instead, it presumably refers to the practice of setting law books and citing legal precedents in blackletter type, a tradition that survived long after the switch to roman and italic text for other printed works.

Instead he painted new works which were passed off as restorations, fooling many experts.

Instead, since development of music involves man's power, it reduces production of food ; furthermore, appreciation of music results in less time for administrative works.

Instead of attending lectures, he spent his student years reading the works of Gauss and Jacobi — the consequence of this being he failed his examinations.

Instead it works with a small number of partner organisations in Sheffield, Dundee and Blackpool to provide a regional presence.

Instead of using a greater number of bits and attempting to record a signal's precise amplitude for every sample cycle, a Direct Stream Digital recorder works by encoding a signal in a series of PWM pulses of fixed amplitude but variable duration and timing.

Instead of the immediate creation ex nihilo, both works postulate a series of emanations of mediums between God and the universe ; and both consider God as the first cause only, and not as the immediate efficient cause of the world.

Instead, he orchestrated some little-known piano works by Tchaikovsky such as The Seasons, along with themes from the opera Cherevichki and the latter part of the symphonic fantasia Francesca da Rimini.

Instead, Johann Adolph Hasse's Mass in D minor was performed, a work with many similarities to Bach's Mass ( the Credo movements in both works feature chant over a walking bass line, for example.

Instead they were valued as finished works of art.

Instead, as most of New York is destroyed, Angel works with Apocalypse's mutant elite, Magneto and his X-Men, and even the Human High Council to maintain and operate a nightclub aptly named Heaven, where humans and mutants can intermingle.

Instead, in 1946 the ceremony was held twice: in January for the works created in 1943-1944 and in June for the works of 1945.

Instead of large-scale canvases, Xul painted on small sheets of paper, sometimes mounting his finished works on sheets of cardboard.

Instead, it is strong and works great things always.

Instead, as in the case of, Studies in Ethnomethodology ( 1967 ), we are given oblique theoretical references to: Wittgenstein Language Philosophy ; Husserl Phenomenology ; Gurwitsch Theory ; the works of the social phenomeonologist Alfred Schutz of the Natural Attitude ; and an assortment of traditional social theorists generally appearing as antipodes and / or sounding boards for ethnomethodological ideas.

Instead, these borrowings are only fragmentary references to theoretical works from which ethnomethodology has " appropriated ", " misread ", and / or, " respecified ", the theoretical ideas of others for the expressed purposes of doing ethnomethodological investigations.

Instead they might learn about some effects in the environment ( i. e., how the tool moves, or how the apparatus works ).

Instead of trying to find out more about his illness, Jack works to set Jennifer up with her old boyfriend, Frankie Brady in order to protect her from the aforementioned Patrick, who he is sure would be after her the moment Jack was gone.

Instead, they propose that politicians should explore ways in which copyright holders can be paid through the movement of their works through P2P networks.

Instead, contempt for the means of grace is the result of " the perverse will of man, which rejects or perverts the means and instrument of the Holy Ghost, which God offers him through the call, and resists the Holy Ghost, who wishes to be efficacious, and works through the Word ..."

Instead, contempt for the means of grace is the result of " the perverse will of man, which rejects or perverts the means and instrument of the Holy Ghost, which God offers him through the call, and resists the Holy Ghost, who wishes to be efficacious, and works through the Word ..."

Instead, construction works began in early 2009 on a new location north-west of the city for a replacement football stadium capable of hosting major international matches.

Instead, Franchitti was contracted by AMG Racing to drive a works Mercedes C-Class in the German Touring Car Championship and the related International Touring Car Championship, where he finished fifth and third respectively.

Instead of giving themselves spontaneously to the orgiastic release that jazz can give them, they undergo psychoanalysis or flirt with mysticism or turn to prostitutes for satisfaction.

Instead of radiators you'll have cooling-heating units, each with its own thermostat.

Instead, he constantly became lost in parts and components of them, confused some of their details with those of neighboring objects, and so on, unless he allowed time to `` trace '' the object in question through minute movements of the head and hands and in this way to discover its contours.

Instead of isolating the literal flatness by specifying and circumscribing it, the pasted paper or cloth releases and spreads it, and the artist seems to have nothing left but this undepicted flatness with which to finish as well as start his picture.

Instead he brought with him the names of some people he had never met and of whom the medium knew nothing.

Instead, the audience can sit back at ease and, from the perspective of an enlightened time which no longer believes in such things, enjoy the dead seriousness with which the characters in the play take the witches and devils which are under discussion.

Instead of linking the nine numbers of this diagram with the traditional Nine Provinces, as was usually done, this equated the odd, Yang numbers with mountains ( firm and resistant, hence Yang ) and the even numbers with rivers ( sinuous and yielding, hence Yin ) ; ;

Instead -- and not just to prove my objectivity -- I hasten to report that it's a highly amusing film which probably does a fairly accurate job of reporting on the Easter vacation shenanigans of collegians down in Fort Lauderdale, and that it seems to come to grips quite honestly with the moral problem that most commonly vexes youngsters in this age group -- that is to say, sex.

Instead the cartoons seem to deal with foibles.

Instead of having a pulp cavity, each tooth has a cluster of thin, upright, parallel tubes of vasodentin ( a modified form of dentine ), with individual pulp canals, held together by cementum.

Instead of starting from theory and applying theory to a particular case, casuists start with the particular case itself and then ask what morally significant features ( including both theory and practical considerations ) ought to be considered for that particular case.

Instead, the irrigated agriculture project was headed for completion with apparently no prospects for extension beyond 2011.

Instead, Rufinus attempted to negotiate with Alaric in person, which only aroused suspicions in Constantinople that Rufinius was in league with the Goths.

Instead, that night ( July 17 / 18 ), Alexios III hid in the palace, and finally, with one of his daughters, Eirene, and such treasures ( 1, 000 pounds of gold ) as he could collect, got into a boat and escaped to Debeltos in Thrace, leaving his wife and his other daughters behind.

Instead of just establishing it as a military prison, he provided for a civil administration, with courts of law.

Instead, AMOS BASIC controlled the computer directly, which caused programs written in it to have a non-standard user interface, and also caused compatibility problems with newer versions of the operating system.

Instead of using Vermin's tired characters, Abner inventively peopled the strip with hillbillies.

Since the 2002 edition, the Apostles ' Creed is included in the Roman Missal with the indication, " Instead of the Niceno-Constantinopolitan Creed, especially during Lent and Easter time, the baptismal Symbol of the Roman Church, known as the Apostles ’ Creed, may be used.

Instead of reviewing music videos, they reviewed ( custom-made ) pages from other Marvel Comics — in one with Ghost Rider, Beavis tries to avoid using the word " fire " to describe the character's fiery skull.

Instead, space itself expands with time everywhere and increases the physical distance between two comoving points.

Instead, it is put in parallel with chapter 4 ( C ) where divine judgements are pronounced against the Babylonian kings.

Instead, the Hebrew name Ahasuerus accords with an inscription of the time that notes that Artaxerxes II was named also Arshu, understood as a shortening of Achshiyarshu the Babylonian rendering of the Persian Khshayarsha ( Xerxes ), through which the Hebrew Achashverosh ( Ahasuerus ) is derived.